U.S. patent number 6,260,282 [Application Number 09/049,801] was granted by the patent office on 2001-07-17 for stage control with reduced synchronization error and settling time.
This patent grant is currently assigned to Nikon Corporation. Invention is credited to Hideyaki Hashimoto, Susumu Makinouchi, Bausan Yuan.
United States Patent |
6,260,282 |
Yuan , et al. |
July 17, 2001 |
**Please see images for:
( Certificate of Correction ) ** |
Stage control with reduced synchronization error and settling
time
Abstract
A positioning system used, by way of example, for lithography,
uses the position of the wafer stage as the trajectory command for
the reticle fine stage control circuit. The reticle fine stage
position is combined with the position of the wafer stage to
generate a synchronous error. The reticle fine stage control
circuit uses a Jacobian differential transformation to convert the
synchronous error into an positional error for the center of
gravity of the reticle fine stage. Thus, any inaccuracies due to
measurement errors caused by rotation of reticle fine stage are
avoided. A controller filter circuit uses the positional error for
the center of gravity to calculate the force on the center of
gravity that will minimize the synchronous error. The controller
filter circuit includes saturation limited integration behavior
that minimizes the settling time. A feedforward loop also generates
a feedforward force, which reduces settling time, and is combined
with the force signal from the controller filter. A force
coordinate transformation circuit receives the summed forces and
calculates the forces to be generated by the actuators connected to
reticle fine stage that will drive reticle fine stage to the
desired position to reduce the synchronous error.
Inventors: |
Yuan; Bausan (San Jose, CA),
Makinouchi; Susumu (Tokyo, JP), Hashimoto;
Hideyaki (Tokyo, JP) |
Assignee: |
Nikon Corporation (Tokyo,
JP)
|
Family
ID: |
21961817 |
Appl.
No.: |
09/049,801 |
Filed: |
March 27, 1998 |
Current U.S.
Class: |
33/1M; 700/263;
700/302; 700/60 |
Current CPC
Class: |
G03F
7/70358 (20130101); G03F 7/70725 (20130101) |
Current International
Class: |
G03F
7/20 (20060101); H01L 021/68 (); G01B 011/00 () |
Field of
Search: |
;33/1M
;364/528.37,528.34,167.06,468.28 ;702/150,151,156,33,44
;356/400,401 ;250/548 ;395/98 ;700/121,263,302,303,60 |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Gutierrez; Diego
Assistant Examiner: Smith; R Alexander
Attorney, Agent or Firm: Skjerven Morrill, MacPherson LLP
Klivans; Norman R. Halbert; Michael J.
Claims
What is claimed is:
1. A positioning apparatus comprising:
a first stage;
a position measurement system positioned near the first stage, said
position measurement system providing a first stage position signal
corresponding to the position of said first stage;
a fine stage positioned above the first stage and coupled to at
least one actuator, wherein said at least one actuator moves said
fine stage in approximate synchronization with said first
stage;
a second position measurement system positioned near the fine
stare, said second position measurement system providing a fine
stage position signal corresponding to the position of said fine
stage; and
a fine stage controller connected with at least one actuator and
receiving a fine stage trajectory command signal proportional to
said first stage position signal, said fine stage controller
generating a positional error signal corresponding to a position of
the center of said fine stage and controlling said at least one
actuator in response to said positional error signal for said
center of said fine stage.
2. The positioning apparatus of claim 1, wherein a multiplier
circuit is disposed between said first stage position measurement
system and said fine stage controller, said multiplier circuit
generating said fine stage trajectory command signal by multiplying
said first stage position signal by a desired reduction ratio.
3. The positioning apparatus of claim 1, further comprising a
coarse stage, wherein said fine stage is movably coupled to said
coarse stage.
4. The positioning apparatus of claim 1, wherein said fine stage
controller comprises:
a position feedback loop combining said fine stage position signal
and said fine stage trajectory command signal to produce a
synchronous error signal reflecting the difference between said
position of said first stage and said position of said fine
stage;
a coordinate transformation circuit converting said synchronous
error signal into said positional error signal for said center of
said fine stage;
a controller filter circuit receiving said positional error signal
corresponding to a position of said center of said fine stage and
in response generating a force signal;
a force coordinate transformation circuit converting said force
signal into a command signal to control said at least one actuator;
and
an amplifier circuit driven by said command signal, said amplifier
circuit generating a control signal controlling said at least one
actuator.
5. The positioning apparatus of claim 4, further comprising a
feedforward loop, said feedforward loop providing a feedforward
force signal in response to said fine stage trajectory command
signal, wherein said feedforward force signal is sunned with said
force signal provided by said controller filter circuit, and said
force coordinate transformation circuit converts the sum of said
force signal and said feedforward force signal into said command
signal.
6. The positioning apparatus of claim 5, said feedforward loop
comprising:
a differentiation circuit receiving said first stage position
signal, said differentiation circuit providing an acceleration
signal equivalent to the second derivative of said fine stage
trajectory command signalwith respect to time;
a feedforward gain circuit receiving said acceleration signal and
in response providing a first feedforward force signal;
a second force coordinate transformation circuit converting said
feedforward force signal into a second feedforward force signal
reflecting the feedforward force on said center of said fine
stage.
7. The positioning apparatus of claim 4, wherein said second
position measurement system measures the differential position of
said fine stage using a first measurement point on said fine stage
to measure the position of said fine stage in a first coordinate
direction, a second measurement point on said fine stage to measure
the position of the left side of said fine stage in a second
coordinate direction, and a third measurement point to measure the
position of the right side of said fine stage in said second
coordinate direction, said second coordinate direction being
orthogonal to said first coordinate direction.
8. The positioning apparatus of claim 7, wherein said coordinate
transformation circuit is a differential Jacobian coordinate
transformation circuit, said Jacobian coordinate transformation
circuit converting said synchronous error signal into said
positional error signal for said center of said fine stage
according to the following equation: ##EQU9##
where the terms .DELTA.x, .DELTA.y, and .DELTA..THETA. are the
positional error of said center of said fine stage, the terms
.DELTA.R.sub.X, .DELTA.R.sub.l, and .DELTA.R.sub.r are the
synchronous error of said fine stage in the respective first
coordinate direction, the right side of said fine stage in said
second coordinate direction, and the left side of said fine stage
in said second coordinate direction, y is the distance in the
second coordinate direction between the measuring point used for
the .DELTA.R.sub.X term and the center line of said fine stage in
said first coordinate direction, a and b are the distances from the
measuring point used for the respective .DELTA.R.sub.1 and
.DELTA.R.sub.r terms and said center line of said fine stage in the
second coordinate direction, and the term 1 is the sum of the a and
b terms.
9. The positioning apparatus of claim 4, wherein said controller
filter circuit includes a saturation limited integration term.
10. The positioning apparatus of claim 9, wherein said saturation
limited integration term is in accordance with the following:
##EQU10##
where I represents the integration function, .DELTA.X is the
positional error term for said center of said fine stage, Ki/s is
the integral with respect to time, and C is a constant.
11. The positioning apparatus of claim 1, wherein said center of
said fine stage is the center of gravity of said fine stage.
12. A method of controlling a fine stage to move synchronously with
a first stage, said method comprising:
controlling the motion of said first stage;
providing a fine stage trajectory command signal that is
proportional to the position of said first stage;
providing a fine stage position signal corresponding to the
position of said fine stage;
generating a synchronous error signal equivalent to the difference
between said fine stage trajectory command signal and said fine
stage position signal; and
controlling the motion of said fine stage in response to said
synchronous error signal, wherein said controlling the motion of
said fine stage comprises:
transforming said synchronous error signal into a positional error
signal for the center of said fine stage;
filtering said positional error signal to generate a force signal
for said center of said fine stage; and
transforming said force signal for said center of said fine stage
into a command signal to control the motion of said fine stage.
13. The method of claim 12, further comprising:
generating a feedforward force signal in response to said fine
stage trajectory command signal; and
summing said force signal and said feedforward force signal;
wherein said transforming said force signal comprises transforming
the sum of said force signal and said feedforward force signal into
said command signal to control the motion of said fine stage.
14. The method of claim 12, wherein transforming said synchronous
error signal into said positional error signal is performed with a
Jacobian differential coordinate transformation.
15. The method of claim 14, wherein said Jacobian differential
coordinate transformation is in accordance with the following
equation: ##EQU11##
where .DELTA.X is equivalent to the positional error for said
center of said fine stage, .DELTA.R is equivalent to the
synchronous error, {tilde over (y)} is a distance in a first
coordinate direction between a first measuring point used in
providing said fine stage position signal and a first center line
of said fine stage in a second coordinate direction, a and b are
the distances in a second coordinate direction between a second
measuring position and a third measuring point, respectively, and a
second center line of said fine stage in said first coordinate
direction, and l is the sum of a and b, wherein said first
coordinate direction and said second coordinate direction are
orthogonal.
16. The method of claim 12, wherein said filtering said positional
error signal to generate a force signal for said center of said
fine stage comprises integrating said positional error signal
wherein the result is saturation limited in accordance with the
following: ##EQU12##
where I represents the integral function, .DELTA.X represents the
positional error of said center of said fine stage, Ki/s is the
integration result, and C is a chosen constant.
17. The method of claim 12, further comprising
amplifying said command signal into a current signal; and
energizing at least one actuator coupled to said fine stage to
generate motion of said fine stage.
18. A positioning apparatus comprising:
a first stage coupled to at least one actuator;
a first stage position measurement apparatus measuring an
off-center differential position of said first stage and producing
a first stage position signal;
a first stage control circuit receiving a is first stage trajectory
command signal, said first stage control circuit comprising:
a position feedback loop providing said first stage position signal
to be combined with said first stage trajectory command signal and
generating a synchronous error signal reflecting the synchronous
error between said off-center differential position of said first
stage and said first stage trajectory command signal;
a differential coordinate transformation circuit receiving said
synchronous error signal and transforming said synchronous error
signal into a positional error signal reflecting the positional
error of the center of said first stage relative to said first
stage trajectory command signal;
a controller filter circuit receiving said positional error signal
and generating a force signal reflecting a force on said center of
said first stage to minimize said positional error; and
a force coordinate transformation circuit receiving said force
signal and generating a command signal to said at least one
actuator.
19. The positioning apparatus of claim 18, further comprising a
second stage, wherein said first stage trajectory command signal is
proportional to the position of said second stage and said first
stage is moved by said at least one actuator in synchronization
with said second stage.
20. The positioning apparatus of claim 18, wherein said
differential coordinate transformation circuit uses a Jacobian
differential transformation.
Description
FIELD OF THE INVENTION
The present invention relates to controlling a stage in a
high-precision positioning instrument and in particular to
controlling a fine stage with minimized synchronization error and
settling time.
BACKGROUND
High-precision positioning instruments are used, for example, in
machining tools, lithography equipment for semiconductor wafer
processing or liquid crystal display devices, or the like. A
control system drives a stage or stages of the positioning
instrument in accordance with a defined path. The path may have one
direction, e.g., the X coordinate direction, or two directions,
e.g., the X and Y coordinate direction s.
Typically in lithography equipment for semiconductor wafer
processing, a first stage is used to position the subject plate
(wafer) in two dimensions, while a separate stage is used to
synchronously position the mask (reticle). The stages are moved
relative to a source of radiant energy and a projection lens to
focus the energy as well as the base structure that supports the
stages. During exposure the stages may be moved either in a
constant velocity "scanning" pattern or in a "step-and-repeat"
pattern.
In a high-precision positioning instrument the stages must be moved
in a synchronous fashion. Where extreme precision is required, such
as in a microlithographic system that produces images on the
sub-micron scale, any misalignment of the stages will result in
defects in the exposed image. Misalignment of the stages is known
as synchronous error.
Conventional positioning instruments typically control the stages
using a velocity feedback system. Thus, the controller of
conventional positioning instruments emphasize velocity control
over control of the position of the stage. A positioning instrument
typically uses velocity information or position information
obtained from a non-center of gravity location on the stage. For
example an interferometer measurement system uses mirrors located
on the sides of the stage. However, a measurement taken with a
mirror on the side of the stage will increase or decrease, while
the position of the center of gravity of the stage may not change,
when the stage is rotated slightly, as illustrated in FIG. 4. Thus,
a velocity error, as well as a positioning error, is possible where
a stage is controlled with information derived from the non-center
of gravity location. Consequently, a stage being controlled with
information obtained from a non-center of gravity location may
develop a synchronous error.
An additional source of synchronous error is caused by a control
system that uses the absolute position of the stage as feedback,
for instance by way of a linear encoder. Because the positioning
system generally uses a single precision 32 bit floating point CPU,
digital signal processor, or a micro-processor, the accuracy of the
measurement is limited to only the 23 bits for the significant
digits "significand." Thus, where the absolute position of the
stage is used as feedback in a control system, the floating point
unit will represent the absolute position of the stage in 23 bits.
Consequently, if the absolute position of the stage is larger than
23 bits, accuracy of the position is lost.
In addition, conventional control systems typically convert the
trajectory command for a stage into a force through the use of a
proportional-integration differentiation (PID) device as is well
known in the art. However, a conventional PID device typically
permits the synchronous error to accumulate during acceleration
periods. After the stage stops accelerating the synchronous error
is reduced. Consequently, a period of time must elapse after the
acceleration period before exposure may begin because the
synchronous error must be eliminated. This time is known as the
settling time of the system and is a limitation on the throughput
of the system.
Thus, a position control system that drives the center of gravity
of the stage with a level of accuracy that is not affected by the
absolute position of the stage is needed to reduce synchronous
error. Moreover, a position control system that limits the
accumulation of synchronous error thereby reducing settling time is
needed.
SUMMARY
A positioning instrument, which may be used in a lithography
machine for example, includes a wafer stage, a reticle coarse
stage, and reticle fine stage connected to the reticle coarse
stage. A position measurement system, such as an interferometer
measurement system, provides the position of the wafer stage that
is used to generate a fine stage trajectory command signal. A
second position measurement system, which may be an interferometer
measurement system, measures the position of the reticle fine
stage. The position of the reticle fine stage is combined with the
fine stage trajectory command and the difference is the synchronous
error of the reticle fine stage.
A fine stage control circuit receives the synchronous error and
uses a Jacobian differential coordinate transformation to convert
the synchronous error into a positional error with respect to the
center of gravity of the reticle fine stage. Thus, the effects of
measuring errors caused by the rotation of the reticle fine stage
may be minimized.
A controller filter uses the positional error to calculate the
forces on the center of gravity of the reticle fine stage that will
minimize the positional error. The controller filter uses a
saturation-limited integrator that limits the integration of the
positional error to a desired constant value. Consequently, the
synchronous error produced during acceleration is limited, thus
reducing the settling time of the system. A feedforward force is
combined with the output of the controller filter to further reduce
the settling time.
The combined force signals are received by a force coordinate
transformation circuit that calculates the forces to be generated
by actuators connected to reticle fine stage and produces a command
signal that controls actuators, which drive reticle fine stage to
the desired position to reduce the synchronous error.
In addition, the synchronous error may be further reduced by using
a single precision floating point digital signal processor,
micro-processor, or the like, where the positions of the wafer
stage and reticle fine stage as well as the synchronous error are
represented as integers.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a perspective view of a positioning instrument in
accordance with one embodiment of the present invention.
FIG. 2 is a block diagram of a control system that minimizes
synchronous error and settling time.
FIG. 3 is a block diagram of a reticle fine stage control system
that minimizes synchronous error and settling time.
FIG. 4 is a top view of a reticle fine stage showing the
relationship between the center of gravity of the reticle fine
stage and the position measurement points.
FIG. 5 is a plot showing the integral term I.DELTA.X along the Y
axis and the term (Ki/s).DELTA.X on the X axis.
FIG. 6A is a plot of the synchronous error .DELTA.R of the reticle
fine stage with respect to time.
FIG. 6B is a plot of the velocity trajectory curve of the reticle
fine stage with respect to time.
FIG. 7 is a top view of the reticle fine stage showing the
relationship of the forces provided by the actuators on the center
of gravity.
FIGS. 8, 8A and 8B are a flowchart indicating the processing
performed by the differential coordinate transformation circuit,
the controller filter circuit, the force coordinate transformation
circuit and the feedforward loop.
DETAILED DESCRIPTION
FIG. 1 is a perspective view of a positioning instrument 100 with a
fine stage 126 that synchronously moves with wafer stage 106.
Positioning instrument 100 is shown as a lithography apparatus for
semiconductor wafer processing. It will be understood, however,
that positioning instrument 100 may be used for any purposes where
high precision positioning is desirable, such as for liquid crystal
display device processing, and is only an exemplary illustration of
the invention.
Positioning instrument 100, as shown in FIG. 1, is supported by a
conventional anti-vibration structure (not shown) and includes a
body 102 with a base 104 attached thereto. A wafer (plate) stage
106 rides on a center beam 108 that is movably connected to base
104 via two side beams 110. Center beam 108 acts as a guide for the
movement of wafer stage 106 in the Y coordinate direction as
illustrated (the arrows are intended only to illustrate the
coordinate directions and are not part of positioning instrument
100).
Center beam 108 rides on two side beams 110, which act as guides
for movement of center beam 108 in the X coordinate direction.
Wafer stage 106 scans in the Y coordinate direction at a constant
velocity, for example 1 cm/sec, and steps a desired distance in the
X coordinate at the beginning or end of each scan. Wafer stage 106
is shown conventionally holding a wafer 112 and mounted on stage
106 are two mirrors 114, 115 used as points of measurement to
measure the position of wafer stage 106, for example with a
conventional interferometer measurement apparatus (not shown).
A reticle (mask) coarse stage 116 is shown positioned above wafer
stage 106, with a conventional projection lens 118 disposed between
reticle coarse stage 116 and wafer stage 106. Reticle coarse stage
116 includes linear motor guides 120 that are used with two
actuators 122, 124 to drive reticle coarse stage 116 at a constant
velocity in the Y coordinate direction. Actuators 122 and 124 may
be linear motors, voice coil motors or electromechanical stepping
motors.
A reticle fine stage 126 is positioned on reticle coarse stage 116
and carries a reticle (mask) 127 in a conventional manner. Reticle
fine stage 126 is vertically supported on reticle coarse stage 116
by anti-friction bearings (not shown), such as air bearings or
roller bearings, as is well known in the art. Four actuators 128,
130, 132, and 134 (actuator 134 is not visible in FIG. 1), such as
voice coil motors, are used to move reticle fine stage 126 in the X
and Y coordinate directions to a desired position.
A planar mirror 136 is attached to reticle fine stage 126 and is
used by an interferometer measurement system (not shown) to provide
a point of measurement for reticle fine stage 126 in the X
coordinate direction. A conventional interferometer measurement
system may be used with planar mirror 136. In addition, two corner
cubed mirrors 138, 140 are mounted on reticle fine stage 126 for
use with an interferometer measurement system (not shown). Corner
cubed mirrors 138 and 140 provide two points of measurement on the
respective left side and right side of reticle fine stage 126 in
the Y coordinate direction. Corner cubed mirrors 138 and 140 are
used together to measure the rotation of reticle fine stage 126 in
the E) (angular rotation) coordinate direction.
To produce an acceptable exposure image, reticle fine stage 126
moves with wafer stage 106 within a desired synchronization range,
while an exposure device (not shown) such as a light source,
illuminates wafer 112 through reticle 127 and projection lens 118.
Wafer stage 106 and reticle coarse stage 116 move at constant
velocities in the Y coordinate direction while reticle fine stage
126 is precisely positioned on reticle coarse stage 116 to correct
for any small deviations from synchronicity with wafer stage 106.
Although both wafer stage 106 and reticle coarse stage 116 move at
constant velocities in the Y coordinate direction, the velocities
of wafer stage 106 and reticle coarse stage 116 need not be the
same. It may be desirable for the velocities of wafer stage 106 and
reticle coarse stage 116 to differ by some proportion to produce a
proportionally reduced exposed image on wafer 112.
A block diagram of a control system 200 for positioning instrument
100 used to maintain . synchronicity between wafer stage 106 and
reticle fine stage 126 is shown in FIG. 2. Control system 200
includes a trajectory command circuit 202, which outputs a command
trajectory signal for the desired positions of wafer stage 106 and
reticle fine stage 126. Trajectory command circuit 202 may be a
digital signal processor, micro-processor, or micro-controller
programmed with the desired trajectory of wafer stage 106. The
command trajectory signals are typically digital signals.
The command trajectory signals are fed directly to wafer stage
control circuit 204. A conventional wafer stage control circuit,
such as a digital signal processor, micro-processor, or
micro-controller as are well known in the art, may be used for
wafer stage control circuit 204. A wafer stage position signal
representing the measured position of wafer stage 106 is fed back
and combined with the command trajectory signal via position
feedback loop 206. The position of wafer stage 106 is determined in
the X and Y coordinate directions via an interferometer measurement
system using mirrors 114, 115 as shown in FIG. 1. The
interferometer measurement system measures the position of wafer
stage 106 relative to a stationary object, such as projection lens
118. Although the present discussion is related to an
interferometer measurement system, it should be understood that
other type of measurement systems, such as a linear encoder, may be
used.
The trajectory command signal from trajectory command block 202 is
also fed to reticle coarse stage control circuit 210. However, the
trajectory command signal is first multiplied by a desired
reduction ratio via multiplier circuit 208, thereby producing a
coarse stage trajectory command signal. It should be understood
that multiplier circuit 208 is part of trajectory command circuit
202 and thus the multiplication of the trajectory command signal by
the desired reduction ratio may be accomplished by the software of
the trajectory command circuit 202. Multiplier circuit 208 is shown
as a separate circuit as an illustration of functionality. Of
course, multiplier circuit 208 may also be a separate device such
as a digital signal processor, micro-processor, or micro-controller
as are well known in the art. As shown in FIG. 2, a multiple of 4
is used for the reduction ratio by multiplier block 208, however,
any reduction ratio may be used and is typically governed by
projection lens 118. However, any reduction ratio may be provided
by multiplier block 208.
The position of reticle coarse stage 116 is determined by an
interferometer measurement system or other appropriate position
measurement device, such as a linear encoder. The position signal
representing the measured position of reticle coarse stage 116 is
combined via feedback loop 212 with the coarse stage trajectory
command signal and received by reticle coarse stage control circuit
210. Reticle coarse stage control circuit 210 may be a conventional
control unit, of the type well known by those of ordinary skill in
the art.
The wafer stage position signal is provided to a reticle fine stage
control circuit 214 via multiplier circuit 216. Multiplier circuit
216 is similar to multiplier circuit 208 and multiplies the wafer
stage position signal by the same reduction ratio as used in
multiplier circuit 208, thereby producing a fine stage trajectory
command signal. Multiplier circuit 216 is implemented within wafer
stage control system 204, however, it may also be implemented
within reticle fine stage control circuit 204.
The fine stage trajectory command signal is combined With a
measured reticle fine stage position via position feedback loop
219. The position of reticle fine stage 126, shown in FIG. 1, is
determined by an interferometer measurement system using planar
mirror 136 and corner cubed mirrors 138 and 140. The position of
reticle fine stage 126 is measured by interferometer measurement
system relative to the same stationary object used to measure the
position of wafer stage 106, e.g., projection lens 118.
Thus, the measured fine stage position signal is combined with the
fine stage trajectory command signal thereby producing a
synchronous error signal. The synchronous error signal reflects the
difference between the fine stage position signal and the fine
stage trajectory command signal, which is the synchronous error AR
between reticle fine stage 126 and the "proportional" position of
wafer stage 106, i.e., the position of wafer stage 106 factoring in
the reduction ratio.
Control system 200 uses the position of wafer stage 106 to generate
the fine stage trajectory command signal. The fine stage trajectory
command signal provides the desired position of reticle fine stage
126, as opposed to a desired velocity or acceleration, where the
desired position is derived directly from the actual position of
wafer stage 106. Consequently, reticle fine stage 126 maintains a
high degree of synchronicity with wafer stage 106. Further, no
velocity or acceleration feedback is necessary.
In addition, a feedforward loop 218, discussed in more detail
below, directly provides the fine stage trajectory command signal
to reticle fine stage control circuit 214. Feedforward loop 218 is
used to reduce the settling time of reticle fine stage 126.
FIG. 3 shows a block diagram of reticle fine stage control circuit
214. Reticle fine stage control circuit 214 receives the fine stage
trajectory command signal which is combined with the measured
reticle fine stage position signal via position feedback loop 219.
Thus, a synchronous error signal reflecting the synchronous error
.DELTA.R is generated.
The synchronous error .DELTA.R of reticle fine stage 126 is
comprised of several synchronous error terms including
.DELTA.R.sub.X representing the synchronous error in the X
coordinate direction of reticle fine stage 126 as measured from the
measuring point on planar mirror 136, .DELTA.R.sub.r representing
the synchronous error in the Y coordinate direction of the right
side of reticle fine stage 126 as measured from mirror 140, and
.DELTA.R.sub.l representing the synchronous error in the Y
coordinate direction of the left side of reticle fine stage 126 as
measured from mirror 138, as shown in FIGS. 1 and 4 (discussed
below).
Interferometer measuring systems are advantageously used to
determine the respective positions of reticle fine stage 126 and
wafer stage 106, because interferometer measuring systems are
differential measurement systems. In other words, the measured
(actual) positions of reticle fine stage 126 and wafer stage 106
are measured in terms of how much the positions have changed.
The synchronous error signal reflecting the synchronous error
.DELTA.R between the proportional position of wafer stage 106 and
reticle fine stage 126 is digital and is represented as an integer.
The use of integers is advantageous because the accuracy level is
increased with the use of a single precision floating point
calculation unit in fine stage control circuit 214. For example, in
a 32 bit floating point unit, 23 bits are typically used as the
significand, or significant digits. Where a small differential
position which is represented as an integer is used, the 23 bits
can accurately represent the position. If the absolute position of
the stage is used instead, accuracy is lost because the absolute
position may be a large value and hence the 23 bits are
inadequate.
The synchronous error signal representing the synchronous error
.DELTA.R is received by a differential coordinate transformation
circuit 220, which generates positional error signal reflecting the
positional error .DELTA.X of the center of gravity of the reticle
fine stage 126. Differential coordinate transformation circuit 220
is a digital signal processor or micro-processor programmed with a
Jacobian coordinate transformation, which is a known coordinate
transformation. The positional error .DELTA.X is comprised of
positional errors terms .DELTA.x, .DELTA.y, and .DELTA..THETA. in
the X, Y, and .THETA. coordinate directions, respectively.
FIG. 4 shows diagramatically the geometric relationship between the
center of gravity C.G. of reticle fine stage 126 and the points
used to measure the position of reticle fine stage 126. As shown in
FIG. 4, a position measurement R.sub.X measures the position of
reticle fine stage 126 in the X coordinate direction at a point on
planar mirror 136, while a position measurement R.sub.r measures
the position of the left side of reticle fine stage 126 in the Y
coordinate direction at a point via corner cubed mirror 138, and a
position measurement R.sub.r measures the position of the right
side of reticle fine stage 126 in the Y coordinate direction at a
point via corner cubed mirror 140.
Where reticle fine stage 126 is orthogonal to the X and Y
coordinate system as illustrated in FIG. 4, the measuring points on
corner cubed mirrors 138 and 140 for position measurements R.sub.l
and R.sub.r are distances a and b, respectively, from a center line
from the center of gravity C.G. of reticle fine stage 126 in the Y
coordinate direction. Moreover, the measuring point on planar
mirror 136 for position measurement R.sub.x is a distance y from a
center line from the center of gravity C.G. of reticle fine stage
126 in the X coordinate direction. Because the measuring point for
position measurement R.sub.X is a point along planar mirror 136, as
reticle fine stage scans in the Y direction, the distance y will
change. The center of gravity C.G. is a distance Lx from the left
side and a distance L.sub.Y from the lead side of reticle fine
stage 126.
As can be seen in FIG. 4, if reticle fine stage 126 rotates in the
.THETA. direction, the position measurements R.sub.X, R.sub.r and
R.sub.l will change despite the position of the center of gravity
C.G. remaining the same. Thus, if reticle fine stage 126 rotates in
the .THETA. direction, it will appear from position measurement
R.sub.X that reticle fine stage 126 moved in the -X coordinate
direction. Further, from position measurement R.sub.r it will
appear that the right side of reticle fine stage 126 moved in the Y
coordinate direction, while from position measurement R.sub.l it
will appear that the left side of reticle fine stage 126 moved in
the -Y coordinate direction. Consequently, for an accurate
measurement of the synchronous error .DELTA.R, the coordinates are
transformed to the center of gravity C.G.
The reticle fine stage position measurement R.sub.X, is combined
with the position measurement of wafer stage 106 in the X
coordinate direction to generate the synchronous error
.DELTA.R.sub.X. Likewise, reticle fine stage position measurements
R.sub.r, and R.sub.l are combined with the position measurement of
wafer stage 106 in the Y coordinate direction to generate
synchronous errors .DELTA.R.sub.r and .DELTA.R.sub.l. In an
alternative embodiment, the position measurements R.sub.r may be
combined with a right side position measurement of wafer stage 106,
while position measurement R.sub.l is combined with a left side
position measurement of wafer stage 106 to generate synchronous
errors .DELTA.R.sub.r and .DELTA.R.sub.l. The distance y is
determined by adding the distance reticle fine stage 126 travels in
the Y coordinate direction with the known position of the center of
gravity C.G. The precise position of the center of gravity C.G. of
reticle fine stage 126 is known because the reticle fine stage 126
starts its movement from a known position in positioning instrument
100. By measuring the incremental changes in the position
measurements R.sub.l and R.sub.r, the distance the center of
gravity C.G. of reticle fine stage 126 travels in the Y coordinate
direction may be determined. Consequently, incremental changes
.DELTA.y of the distance y can be determined and summed with the
last known distance y.sub.0. Thus, the distance y between the
center line from the center of gravity C.G. of reticle fine stage
126 and the measuring point for position measurement R.sub.X is
known.
The positional errors .DELTA.x, .DELTA.y, and .DELTA..THETA. of the
center of gravity C.G. and distance y may be related to the
synchronous errors .DELTA.R.sub.x, .DELTA.R.sub.l, and
.DELTA.R.sub.r by the following: ##EQU1##
where L.sub.X is the distance of the center of gravity C.G. from
the left side of reticle fine stage 126, y is the distance between
the measuring point for position measurement R.sub.X and a center
line from the center of gravity C.G. of reticle fine stage 126 in
the X coordinate direction, a and b are the respective distances
between the measuring points for position measurements R.sub.l and
R.sub.r, respectively, and a center line from the center of gravity
C.G. of reticle fine stage 126 in the Y coordinate direction.
Because any rotation in the .THETA. direction of reticle fine stage
126 will be small, the term (.DELTA..THETA.).sup.2 will be very
small and may be ignored. Therefore, the equ. 1 above may be
approximated as: ##EQU2##
Where the terms .DELTA.R.sub.X, .DELTA.R.sub.l, and .DELTA.R.sub.r
comprise the synchronous error .DELTA.R and the terms .DELTA.x,
.DELTA.y, and .DELTA..THETA. comprise the term .DELTA.X, equ. 2 may
be expressed as:
where J is a Jacobian relationship.
As shown in FIG. 3, differential coordinate transformation circuit
220 receives synchronous error .DELTA.R and produces the positional
error .DELTA.X for the center. of gravity C.G. Thus, differential
coordinate transformation circuit 220 is programmed to solve for
.DELTA.X according to the following:
or: ##EQU3##
where l=a+b.
Thus, differential coordinate transformation circuit 220 shown in
FIG. 3 is programmed to determine the positional error .DELTA.X of
the center of gravity C.G. of reticle fine stage 126 and generate a
corresponding positional error signal using the Jacobian
transformation shown in equ. 4. The coding of software to implement
the Jacobian coordinate transformation of equ. 4 in differential
coordinate transformation circuit 220 is well within the knowledge
of those of ordinary skill in the art in light of the present
disclosure.
The position error signal generated by differential coordinate
transformation circuit 220 is received by a controller filter
circuit 222. Controller filter circuit 222 provides a proportional
gain (Kp) plus a saturation-limited integral action (I), followed
by a lead filter. Mathematically controller filter block 222
provides a filtered position of the center of gravity C.G. as
follows: ##EQU4##
where Fx is the force on the center of gravity C.G. required to
minimize the positional error .DELTA.x, Kp is a proportional gain
term, I is a saturation-limited integral term, s+a/s+b is a lead
filter term using a Laplace transform, and .DELTA.X is the
positional error of the center of gravity C.G. Where the position
signals for wafer stage 106 and reticle fine stage 126 are
integers, the positional error signals will be integers. Thus,
controller filter circuit 222 uses discrete proportional gain,
integration and lead filter functions.
Controller filter circuit 222 uses a saturation limited integral
term I, which reduces settling time of the system. FIG. 5 shows a
plot of the integral term I.DELTA.X along the Y axis and the term
(Ki/s).DELTA.X on the X axis, where Ki is the integral with respect
to time, and s is the Laplace transform. The constant C is an
empirical value chosen to limit saturation of the integral term.
The saturation limited integral functions as shown below.
##EQU5##
Thus, the integral I.DELTA.X is limited to .+-.C and values in
between.
FIG. 6A shows a plot of the synchronous error AR along the Y axis
and time along the X axis. FIG. 6B shows the velocity curve of
reticle fine stage 126, where the Y axis represents velocity and
the X axis represents time. As shown in FIG. 6B, reticle fine stage
126 accelerates from time t.sub.0 until a time t.sub.exp at which
time reticle fine stage 126 has a constant velocity Vc and the
exposure of wafer 112 (shown in FIG. 1) begins.
Curve 250 in FIG. 6A represents the synchronous error .DELTA.R
where a conventional integration component is used in controller
filter circuit 222. As shown in FIG. 6A, curve 250 remains
positively saturated until time t.sub.exp at which time the
synchronous error .DELTA.R curve 250 overshoots zero and becomes
negative. Thus, a settling period is required by curve 250 during
which the synchronous error .DELTA.R is allowed to approach zero
after acceleration of reticle fine stage 126 has stopped.
However, where the integration component has a saturation limit as
described in equ. 6, a synchronous M error .DELTA.R as represented
by curve 260 is generated. Although curve 260 has a higher
amplitude than curve 250, the synchronous error .DELTA.R
represented by curve 260 decreases quickly. Thus, at time t.sub.exp
curve 260 has a value of approximately zero. Consequently, curve
260 has a fast settling time. The settling time of curve 260 may be
varied by adjusting the constant C in equ. 6.
Controller filter circuit 222 is thus programmed to generate a
force signal reflecting the force Fx on the center of gravity C.G.
of reticle fine stage 126 that will minimize the positioning error
.DELTA.X as per equations 5 and 6. The coding of software to
implement a conventional proportional gain (Kp), a
saturation-limited integral action (I) according to equ. 6, and a
lead filter function in controller filter circuit 222 is well
within the knowledge of those of ordinary skill in the art in light
of the present disclosure.
As shown in FIG. 3, the force signal Fx from controller filter
circuit 222 is combined with a feedforward force signal and the sum
Fsum is received by a force coordinate transformation circuit 224.
Force coordinate transformation circuit 224 converts the summed
force signal from controller filter 222 and feedforward force
signal to a command signal that reflects the force Fm that is to be
generated by actuators 128, 130, 132, and 134, shown in FIG. 1 and
7 below, to drive the center of gravity C.G. of reticle fine stage
126 to the desired position. The command signal generated by force
coordinate transformation circuit 224 is used to control amplifier
226, which drives actuators 128, 130, 132, and 134. Force
coordinate transformation block circuit 224 may be a conventional
digital signal processor, micro-processor or the like.
FIG. 7 shows a simplified top (plan) view of reticle fine stage 126
with the forces provided by actuators 128, 130, 132, and 134. As
shown in FIG. 7, actuators 128, 130, 132, and 134, which may be
voice coil motors, provide respective forces F.sub.l, F.sub.x1,
F.sub.x2, and F.sub.r on the center of gravity C.G. of reticle fine
stage 126. It should be understood that actuators 128, 130, 132,
and 134 may also provide the opposite of these forces, i.e.,
-F.sub.l, -F.sub.xl, -F.sub.x2, and -F.sub.r.
Actuators 130 and 132 each provide a respective force F.sub.x1 and
F.sub.x2, which in conjunction provide a net force F.sub.X on the
center of gravity C.G. of reticle fine stage 126, as the force
coordinate system in FIG. 7 illustrates. Likewise, actuators 128
and 134 each provide forces F.sub.l and F.sub.r which in
conjunction generate a net force F.sub.Y on the center of gravity
C.G. in the Y coordinate direction. Actuators 128 through 134 may
also provide a net torque T.sub..theta. on reticle fine stage 126
to provide accelerate reticle fine stage 126 in the 0
direction.
As shown in FIG. 7, the center of gravity C.G. of reticle fine
stage 126 is not necessarily in the center of reticle fine stage
126. The center of gravity C.G. has a distance l.sub.1 from the
force applied by actuator 130, a distance l.sub.2 from the force
applied by actuator 132, a distance l.sub.3 from the force applied
by actuator 134, and a distance l.sub.4 from the force applied by
actuator 128. By way of an example, the distances between the
center of gravity C.G. and forces applied by the individual
actuators are: l.sub.1 =0.1488 m, l.sub.2 =0.1532 m, l.sub.3
=0.1717 m, and l.sub.4 =0.1463.
The net forces on the center of gravity C.G. of reticle fine stage
126 may be expressed as follows: ##EQU6##
where M is the mass of reticle fine stage 126, approximately 4 kg,
and I is the moment of inertia of reticle fine stage 126,
approximately 6.68E.sup.-2 kg/m.sup.2, and the term d.sup.2
/dt.sup.2 is the second derivative with respect to time.
The forces to be produced by actuators 128, 130, 132, and 134 may
generate net forces F.sub.X, F.sub.Y, and T.sub..THETA. on the
center of gravity C.G. of reticle fine stage 126 according to the
following: ##EQU7##
The forces F.sub.X1 and F.sub.X2 generated by actuators 130 and 132
may each produce half of the net force F.sub.X, which may be
expressed as:
The forces F.sub.l and F.sub.r needed to generate the desired net
forces F.sub.Y and T.sub..THETA. may then be found by inverting
equ. 8 as follows: ##EQU8##
Thus, force coordinate transformation circuit 224 is programmed
with equations 9, 10, and 11 to generate the command signal with
the forces to be generated by each actuator to move reticle fine
stage 126 to the desired position. The coding of software to
implement equations 9, 10, and 11 within force coordinate
transformation circuit 224 is well within the knowledge of those of
ordinary skill in the art in light of the present disclosure.
The command signal produced by force coordinate transformation
circuit 224 controls amplifier 226 as shown in FIG. 3. Amplifier
226 is a conventional current mode amplifier. A current mode
amplifier is used because if voice coil motors or linear motors are
used as actuators 128, 130, 132, and 134 the output force is
constantly proportional to the input current. Amplifier 226, thus,
generates current signals that drive actuators 128 through 134,
which in response move reticle fine stage 126 to the desired
position.
Reticle fine stage control circuit 204 also includes a feedforward
loop 231, including a differentiation circuit 230, a feedforward
gain circuit 232, and a force coordinate transformation circuit
234. Feedforward loop 231 is a digital signal processor,
micro-processor or the like. Feedforward loop 231 receives fine
stage trajectory command signal via line 218. The fine stage
trajectory command signal is differentiated twice with respect to
time by a conventional differentiation circuit 230. Thus,
differentiation circuit 230 generates an acceleration signal. The
coding of software to generate an acceleration signal with
differentiation circuit 230 is well within the knowledge of those
of ordinary skill in the art.
The acceleration signal is received by a feedforward gain circuit
232, which generates a gain in the acceleration signal. Feedforward
gain circuit 232 thus generates a feedforward signal representing
the desired feedforward acceleration of reticle fine stage 126.
Feedforward gain circuit 232 generates a variable gain in the
acceleration signal depending on whether wafer stage 106, shown in
FIG. 1, is accelerating, decelerating, or depending on the weight
of the reticle fine stage 126. Feedforward gain circuit 232 may
also produce a constant gain if desired.
The feedforward signal from feedforward gain circuit 232 is
received by a force coordinate transformation circuit 234. Force
coordinate transformation circuit 234 may be a digital signal
processor, micro-processor or the like. Force coordinate
transformation circuit 234 used in the feedforward loop 231
produces a feedforward force signal reflecting the desired
feedforward force on the center of gravity C.G. of reticle fine
stage 126. by transforming the force signal generated by
differential circuit 230 and feedforward gain circuit 232 into the
center of gravity C.G. reference frame using the Jacobian
transformation of equ. 4. The feedforward force signal from the
force coordinate transformation block 234 is then summed with the
force Fx on the center of gravity C.G. of reticle fine stage 126
produced by controller filter circuit 222 generating a summed force
signal Fsum, which is then provided to force coordinate
transformation circuit 224 as described above.
As those of ordinary skill in the art will understand, most of
reticle fine stage control circuit 204, including differential
coordinate transformation circuit 220, controller filter 222, force
coordinate transformation circuit 224, differentiation circuit 230,
feedforward gain circuit 232, and force coordinate transformation
circuit 234 may be part of the same digital signal processor, or
micro-processor running off the same software code. FIGS. 8, 8A and
8B are a self explanatory flowchart 300 depicting the processing of
reticle fine stage control circuit 204. As shown in flowchart 300,
processing begins and the coordinate transformation described in
reference to differential coordinate transformation circuit 220
occurs in steps 302 to 308. The processing of controller filter
circuit 222 is described in flowchart 300 in steps 310 to 324. The
processing of feedforward loop 231 is described in steps 326 to
330. Finally, the summing of force Fx and feedforward force as well
as the processing of force coordinate transformation circuit 224 is
shown in steps 332 and 334. The coding of software to implement the
above functions is well within the skill of those in the art in
light of the present disclosure.
Although the present invention has been described in considerable
detail with reference to certain versions thereof, other versions
are possible. For example, reticle fine stage 126 may be controlled
with a greater or lesser number of actuators. One having ordinary
skill in the art will be able to adapt force coordinate
transformation circuit 224 for the use of a different number of
actuators. Additionally, force coordinate transformation circuit
224 may use alternative methods of deriving the forces to be
generated by each actuator. Positioning system 100 is not
restricted to the system shown in FIG. 1. Positioning system 100
may have a fine stage on the wafer stage 106, or positioning
instrument 100 may use a reticle fine stage that is not coupled to
a coarse stage. Further, the manner of measuring the positions of
the stages may be adapted to any appropriate manner and is not
limited specifically to an interferometer measuring system.
Therefore, the spirit and scope of the appended claims should not
be limited to the description of the versions depicted in the
figures.
* * * * *